The Diagonals Of A Rhombus ABCD Intersect At O. Taking ‘O’ As The Centre, An Arc Of Radius 6 Cm Is Drawn Intersecting OA And OD At E And F Respectively. The Area Of The Sector OEF Is : (A) 9p Cm2 (C) 12p Cm2 (B) 3p Cm2 (D) 18p Cm2
**The Diagonals of a Rhombus: A Geometric Exploration**
A rhombus is a type of quadrilateral where all four sides are of equal length. In this article, we will explore the properties of a rhombus and how the diagonals intersect at a point O. We will also discuss the concept of a sector and how to calculate its area.
A rhombus is a quadrilateral with all sides of equal length. The diagonals of a rhombus bisect each other at right angles. In this case, the diagonals AC and BD intersect at point O.
Taking O as the centre, an arc of radius 6 cm is drawn. This arc intersects OA and OD at points E and F respectively.
To calculate the area of the sector OEF, we need to use the formula:
Area of sector = (θ/360) × πr^2
where θ is the angle subtended by the sector at the centre, and r is the radius of the arc.
θ (Angle Subtended by the Sector)
Since the arc intersects OA and OD at points E and F respectively, the angle subtended by the sector at the centre is 60° (as the diagonals of a rhombus bisect each other at right angles).
r (Radius of the Arc)
The radius of the arc is given as 6 cm.
Calculating the Area
Now, we can calculate the area of the sector OEF using the formula:
Area of sector = (60/360) × π(6)^2 = (1/6) × 3.14 × 36 = 18.84 cm^2
In this article, we explored the properties of a rhombus and how the diagonals intersect at a point O. We also discussed the concept of a sector and how to calculate its area. The area of the sector OEF is approximately 18.84 cm^2.
Q: What is a rhombus?
A: A rhombus is a type of quadrilateral where all four sides are of equal length.
Q: What is the angle subtended by the sector OEF at the centre?
A: The angle subtended by the sector OEF at the centre is 60°.
Q: What is the radius of the arc?
A: The radius of the arc is 6 cm.
Q: How to calculate the area of the sector OEF?
A: To calculate the area of the sector OEF, we use the formula: Area of sector = (θ/360) × πr^2, where θ is the angle subtended by the sector at the centre, and r is the radius of the arc.
Q: What is the area of the sector OEF?
A: The area of the sector OEF is approximately 18.84 cm^2.
Q: What is the formula to calculate the area of a sector?
A: The formula to calculate the area of a sector is: Area of sector = (θ/360) × πr^2, where θ is the angle subtended by the sector at the centre, and r is the radius of the arc.